This is most likely worn by enlisted personnel (E-1 to E-9) who are Mission Specialists on spacecraft.
These personnel can be involved in Earth orbital activities, as well as being stationed on any of the Moon Bases, Mars Bases or other Deep Space activities.

These wings are an integral part of the rank insignia as well as a qualification badge (worn on the front of the jacket, shirt, etc.)

I was interested in Sunita Williams' "running" the Boston Marathon from the International Space Station, and found out she's a Commander (O-5) in the U.S. Navy. Although she's a Naval Aviator, she's basically an engineer and helicopter pilot. On the Shuttle and the ISS she's a flight engineer. So would she wear non-pilot spacecrew wings?

Actually, good question: do Navy, Marine, and Air Force aviators wear special wings once they've been in space? I once read about astronaut's wings being awarded to the X-15 pilot who rose above 50 nautical miles above sea level.

Hey there, great question. She would more likely than not be wearing an Astronaut variant of the Naval Flight Officer wings. The only difference between the NA and NFO wings are the crossed anchors behind the shield as opposed to a single verticle anchor centered behind the shield.

Furthermore, all those who have qualified as astronauts by a certain degree replace their flight insignia, the shield containing a shooting star rather than the traditional US Flag Emblem. And for Chuck, all Naval Aircrew, both commissioned and enlisted wear Gold wings. But the design is very cool! This may spark some more interest in the progressing chance of regular folks going into the last frontier.